Question: $86$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $58$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 86}$ ${x = 3y-58}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-58}$ for $x$ in the first equation. ${(3y-58)}{+ y = 86}$ Simplify and solve for $y$ $ 3y-58 + y = 86 $ $ 4y-58 = 86 $ $ 4y = 144 $ $ y = \dfrac{144}{4} $ ${y = 36}$ Now that you know ${y = 36}$ , plug it back into ${x = 3y-58}$ to find $x$ ${x = 3}{(36)}{ - 58}$ $x = 108 - 58$ ${x = 50}$ You can also plug ${y = 36}$ into ${x+y = 86}$ and get the same answer for $x$ ${x + }{(36)}{= 86}$ ${x = 50}$ There were $50$ home team fans and $36$ away team fans.